def resp_spectrum(source, resp_file, downsamp_freq):
'''
remove the instrument response with response spectrum from evalresp.
the response spectrum is evaluated based on RESP/PZ files and then
inverted using obspy function of invert_spectrum.
'''
#--------resp_file is the inverted spectrum response---------
respz = np.load(resp_file)
nrespz = respz[1][:]
spec_freq = max(respz[0])
#-------on current trace----------
nfft = _npts2nfft(source.stats.npts)
sps = source.stats.sample_rate
#---------do the interpolation if needed--------
if spec_freq < 0.5 * sps:
raise ValueError(
'spectrum file has peak freq smaller than the data, abort!')
else:
indx = np.where(respz[0] <= 0.5 * sps)
nfreq = np.linspace(0, 0.5 * sps, nfft)
nrespz = np.interp(nfreq, respz[0][indx], respz[1][indx])
#----do interpolation if necessary-----
source_spect = np.fft.rfft(source.data, n=nfft)
#-----nrespz is inversed (water-leveled) spectrum-----
source_spect *= nrespz
source.data = np.fft.irfft(source_spect)[0:source.stats.npts]
return source
def convolve(trace, transfer_function, pre_filt=False):
# write data to a numpy array
data = trace.data
npts = len(data)
nfft = _npts2nfft(npts)
# Transform data to frequency domain
data = np.fft.rfft(data, n=nfft)
# find the frequencies corresponding to each element of the fft
delta = trace.stats.delta
fy = 1. / (delta * 2.0)
# start at zero to get zero for offset/ DC of fft
frequencies = np.linspace(0, fy, nfft // 2 + 1)
# pre-filter the data
if pre_filt:
freq_domain_taper = cosine_sac_taper(frequencies, flimit=pre_filt)
data *= freq_domain_taper
# perform the convolution
data *= transfer_function(frequencies)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:npts]
# write data back into trace
trace.data = data
def filter_synt(tr, pre_filt):
"""
Perform a frequency domain taper like during the response removal
just without an actual response...
:param tr:
:param pre_filt:
:return:
"""
data = tr.data.astype(np.float64)
# smart calculation of nfft dodging large primes
nfft = _npts2nfft(len(data))
fy = 1.0 / (tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
data *= c_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0 : len(data)]
# assign processed data and store processing information
tr.data = data
def filter_trace(tr, pre_filt):
"""
Perform a frequency domain taper mimicing the behavior during the
response removal, without a actual response removal.
:param tr: input trace
:param pre_filt: frequency array(Hz) in ascending order, to define
the four corners of filter, for example, [0.01, 0.1, 0.2, 0.5].
:type pre_filt: Numpy.array or list
:return: filtered trace
"""
if type(tr) != obspy.Trace:
raise ValueError("First Argument should be trace: %s" % type(tr))
if not check_array_order(pre_filt):
raise ValueError("Frequency band should be in ascending order: %s"
% pre_filt)
data = tr.data.astype(np.float64)
# smart calculation of nfft dodging large primes
nfft = _npts2nfft(len(data))
fy = 1.0 / (tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
data *= c_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:len(data)]
# assign processed data and store processing information
tr.data = data
def filter_trace(tr, pre_filt):
"""
Perform a frequency domain taper mimicing the behavior during the
response removal, without a actual response removal.
:param tr: input trace
:param pre_filt: frequency array(Hz) in ascending order, to define
the four corners of filter, for example, [0.01, 0.1, 0.2, 0.5].
:type pre_filt: Numpy.array or list
:return: filtered trace
"""
if not isinstance(tr, Trace):
raise TypeError("First Argument should be trace: %s" % type(tr))
if not check_array_order(pre_filt):
raise ValueError("Frequency band should be in ascending order: %s" %
pre_filt)
data = tr.data.astype(np.float64)
# smart calculation of nfft dodging large primes
nfft = _npts2nfft(len(data))
fy = 1.0 / (tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
data *= c_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:len(data)]
# assign processed data and store processing information
tr.data = data
def process_function(st, inv):
st.detrend("linear")
st.detrend("demean")
st.taper(max_percentage=0.05, type="hann")
# Perform a frequency domain taper like during the response removal
# just without an actual response...
for tr in st:
data = tr.data.astype(np.float64)
# smart calculation of nfft dodging large primes
from obspy.signal.util import _npts2nfft
nfft = _npts2nfft(len(data))
fy = 1.0 / (tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
data *= c_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:len(data)]
# assign processed data and store processing information
tr.data = data
st.detrend("linear")
st.detrend("demean")
st.taper(max_percentage=0.05, type="hann")
st.interpolate(sampling_rate=sampling_rate,
starttime=starttime,
npts=npts)
components = [tr.stats.channel[-1] for tr in st]
if "N" in components and "E" in components:
station_latitude = inv[0][0].latitude
station_longitude = inv[0][0].longitude
_, baz, _ = gps2DistAzimuth(station_latitude, station_longitude,
event_latitude, event_longitude)
st.rotate(method="NE->RT", back_azimuth=baz)
# Convert to single precision to save space.
for tr in st:
tr.data = np.require(tr.data, dtype="float32")
return st
def process_function(st, inv):
st.detrend("linear")
st.detrend("demean")
st.taper(max_percentage=0.05, type="hann")
# Perform a frequency domain taper like during the response removal
# just without an actual response...
for tr in st:
data = tr.data.astype(np.float64)
# smart calculation of nfft dodging large primes
from obspy.signal.util import _npts2nfft
nfft = _npts2nfft(len(data))
fy = 1.0 / (tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
data *= c_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:len(data)]
# assign processed data and store processing information
tr.data = data
st.detrend("linear")
st.detrend("demean")
st.taper(max_percentage=0.05, type="hann")
st.interpolate(sampling_rate=sampling_rate, starttime=starttime,
npts=npts)
components = [tr.stats.channel[-1] for tr in st]
if "N" in components and "E" in components:
station_latitude = inv[0][0].latitude
station_longitude = inv[0][0].longitude
_, baz, _ = gps2DistAzimuth(station_latitude, station_longitude,
event_latitude, event_longitude)
st.rotate(method="NE->RT", back_azimuth=baz)
# Convert to single precision to save space.
for tr in st:
tr.data = np.require(tr.data, dtype="float32")
return st
def process_synthetics(self):
lowpass_freq = 1 / 60.
highpass_freq = 1 / 120.
freqmin = highpass_freq
freqmax = lowpass_freq
f2 = highpass_freq
f3 = lowpass_freq
f1 = 0.8 * f2
f4 = 1.2 * f3
pre_filt = (f1, f2, f3, f4)
self.tr.differentiate()
# self.tr.data = convolve_stf(self.tr.data)
self.tr.detrend("linear")
self.tr.detrend("demean")
self.tr.taper(max_percentage=0.05, type="hann")
# Perform a frequency domain taper like during the response removal
# just without an actual response...
data = self.tr.data.astype(np.float64)
orig_len = len(data)
# smart calculation of nfft dodging large primes
from obspy.signal.util import _npts2nfft
from obspy.signal.invsim import c_sac_taper
nfft = _npts2nfft(len(data))
fy = 1.0 / (self.tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
data *= c_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:orig_len]
# assign processed data and store processing information
self.tr.data = data
def sync_remove_response(pre_filt, st):
"""
mimic obspy.remove_response, but only do the frequency taper
"""
for trace in st:
data = trace.data.astype(np.float64)
npts = len(data)
nfft = _npts2nfft(npts)
data = np.fft.rfft(data, n=nfft)
t_samp = trace.stats.delta
fy = 1 / (t_samp * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1).astype(np.float64)
freq_domain_taper = obspy.signal.invsim.cosine_sac_taper(
freqs, flimit=pre_filt)
data *= freq_domain_taper
data = np.fft.irfft(data)[0:npts]
trace.data = data
return st
def pre_filter(stream, pre_filt=(0.02, 0.05, 8.0, 10.0)):
"""
Applies the same filter as remove_response without actually removing the
response.
"""
for tr in stream:
data = tr.data.astype(np.float64)
nfft = _npts2nfft(len(data))
fy = 1.0 / (tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
data *= c_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:tr.stats.npts]
# assign processed data and store processing information
tr.data = data
return stream
def pre_filter(stream, pre_filt=(0.02, 0.05, 8.0, 10.0)):
"""
Applies the same filter as remove_response without actually removing the
response.
"""
for tr in stream:
data = tr.data.astype(np.float64)
nfft = _npts2nfft(len(data))
fy = 1.0 / (tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
data *= cosine_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:len(data)]
# assign processed data and store processing information
tr.data = data
return stream
def convolve(trace, func):
from obspy.signal.util import _npts2nfft
from obspy.signal.invsim import cosine_sac_taper
data = trace.data
delta = trace.stats.delta
npts = len(data)
nfft = _npts2nfft(npts)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
fy = 1. / (delta * 2.0)
# start at zero to get zero for offset/ DC of fft
freqs = np.linspace(0, fy, nfft // 2 + 1)
freq_response = func(freqs)
if pre_filt:
freq_domain_taper = cosine_sac_taper(freqs, flimit=pre_filt)
data *= freq_domain_taper
'''
if water_level is None:
# No water level used, so just directly invert the response.
# First entry is at zero frequency and value is zero, too.
# Just do not invert the first value (and set to 0 to make sure).
freq_response[0] = 0.0
freq_response[1:] = 1.0 / freq_response[1:]
else:
# Invert spectrum with specified water level.
invert_spectrum(freq_response, water_level)
'''
data *= freq_response
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:npts]
def filter_synt(tr, pre_filt):
"""
Perform a frequency domain taper like during the response removal
just without an actual response...
:param tr:
:param pre_filt:
:return:
"""
data = tr.data.astype(np.float64)
# smart calculation of nfft dodging large primes
nfft = _npts2nfft(len(data))
fy = 1.0 / (tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
data *= cosine_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:len(data)]
# assign processed data and store processing information
tr.data = data
def convolve_stf(stf: np.array, data: np.array, nfft=None):
# conv = np.convolve(stf, data, mode="same")
from scipy import signal
# recovered, remainder = signal.deconvolve(data, stf)
from obspy.signal.util import _npts2nfft
import math
if nfft is None:
nfft = _npts2nfft(npts=len(data))
stf_conv_f = np.fft.rfft(stf, n=nfft)
# Apply a 5 percent, at least 5 samples taper at the end.
# The first sample is guaranteed to be zero in any case.
tlen = max(int(math.ceil(0.05 * len(data))), 5)
taper = np.ones_like(data)
taper[-tlen:] = signal.hann(tlen * 2)[tlen:]
dataf = np.fft.rfft(taper * data, n=nfft)
f = stf_conv_f
recovered = np.fft.irfft(dataf * f)[:nfft]
return recovered
def remove_response2(self, inventory=None, output="VEL", water_level=60,
pre_filt=None, zero_mean=True, taper=True,
taper_fraction=0.05, plot=False, fig=None, **kwargs):
"""
EDIT OF OBSPY'S REMOVE_RESPONSE FUNCTION
Including titles etc.
Deconvolve instrument response.
Uses the adequate :class:`obspy.core.inventory.response.Response`
from the provided
:class:`obspy.core.inventory.inventory.Inventory` data. Raises an
exception if the response is not present.
Note that there are two ways to prevent overamplification
while convolving the inverted instrument spectrum: One possibility is
to specify a water level which represents a clipping of the inverse
spectrum and limits amplification to a certain maximum cut-off value
(`water_level` in dB). The other possibility is to taper the waveform
data in the frequency domain prior to multiplying with the inverse
spectrum, i.e. perform a pre-filtering in the frequency domain
(specifying the four corner frequencies of the frequency taper as a
tuple in `pre_filt`).
.. note::
Any additional kwargs will be passed on to
:meth:`obspy.core.inventory.response.Response.get_evalresp_response`,
see documentation of that method for further customization (e.g.
start/stop stage).
.. note::
Using :meth:`~Trace.remove_response` is equivalent to using
:meth:`~Trace.simulate` with the identical response provided as
a (dataless) SEED or RESP file and when using the same
`water_level` and `pre_filt` (and options `sacsim=True` and
`pitsasim=False` which influence very minor details in detrending
and tapering).
.. rubric:: Example
>>> from obspy import read, read_inventory
>>> st = read()
>>> tr = st[0].copy()
>>> inv = read_inventory()
>>> tr.remove_response(inventory=inv) # doctest: +ELLIPSIS
<...Trace object at 0x...>
>>> tr.plot() # doctest: +SKIP
.. plot::
from obspy import read, read_inventory
st = read()
tr = st[0]
inv = read_inventory()
tr.remove_response(inventory=inv)
tr.plot()
Using the `plot` option it is possible to visualize the individual
steps during response removal in the frequency domain to check the
chosen `pre_filt` and `water_level` options to stabilize the
deconvolution of the inverted instrument response spectrum:
>>> from obspy import read, read_inventory
>>> st = read("/path/to/IU_ULN_00_LH1_2015-07-18T02.mseed")
>>> tr = st[0]
>>> inv = read_inventory("/path/to/IU_ULN_00_LH1.xml")
>>> pre_filt = [0.001, 0.005, 45, 50]
>>> tr.remove_response(inventory=inv, pre_filt=pre_filt, output="DISP",
... water_level=60, plot=True) # doctest: +SKIP
<...Trace object at 0x...>
.. plot::
from obspy import read, read_inventory
st = read("/path/to/IU_ULN_00_LH1_2015-07-18T02.mseed", "MSEED")
tr = st[0]
inv = read_inventory("/path/to/IU_ULN_00_LH1.xml", "STATIONXML")
pre_filt = [0.001, 0.005, 45, 50]
output = "DISP"
tr.remove_response(inventory=inv, pre_filt=pre_filt, output=output,
water_level=60, plot=True)
:type inventory: :class:`~obspy.core.inventory.inventory.Inventory`
or None.
:param inventory: Station metadata to use in search for adequate
response. If inventory parameter is not supplied, the response
has to be attached to the trace with :meth:`Trace.attach_response`
beforehand.
:type output: str
:param output: Output units. One of:
``"DISP"``
displacement, output unit is meters
``"VEL"``
velocity, output unit is meters/second
``"ACC"``
acceleration, output unit is meters/second**2
:type water_level: float
:param water_level: Water level for deconvolution.
:type pre_filt: list or tuple of four float
:param pre_filt: Apply a bandpass filter in frequency domain to the
data before deconvolution. The list or tuple defines
the four corner frequencies `(f1, f2, f3, f4)` of a cosine taper
which is one between `f2` and `f3` and tapers to zero for
`f1 < f < f2` and `f3 < f < f4`.
:type zero_mean: bool
:param zero_mean: If `True`, the mean of the waveform data is
subtracted in time domain prior to deconvolution.
:type taper: bool
:param taper: If `True`, a cosine taper is applied to the waveform data
in time domain prior to deconvolution.
:type taper_fraction: float
:param taper_fraction: Taper fraction of cosine taper to use.
:type plot: bool or str
:param plot: If `True`, brings up a plot that illustrates how the
data are processed in the frequency domain in three steps. First by
`pre_filt` frequency domain tapering, then by inverting the
instrument response spectrum with or without `water_level` and
finally showing data with inverted instrument response multiplied
on it in frequency domain. It also shows the comparison of
raw/corrected data in time domain. If a `str` is provided then the
plot is saved to file (filename must have a valid image suffix
recognizable by matplotlib e.g. '.png').
"""
# limit_numpy_fft_cache()
from obspy.core.inventory import PolynomialResponseStage
from obspy.signal.invsim import (cosine_taper, cosine_sac_taper,
invert_spectrum)
if plot:
import matplotlib.pyplot as plt
if (isinstance(inventory, (str, native_str)) and
inventory.upper() in ("DISP", "VEL", "ACC")):
from obspy.core.util.deprecation_helpers import ObsPyDeprecationWarning
output = inventory
inventory = None
msg = ("The order of optional parameters in method "
"remove_response has changed. 'output' is not accepted "
"as first positional argument in the next release.")
warnings.warn(msg, category=ObsPyDeprecationWarning, stacklevel=3)
response = self._get_response(inventory)
# polynomial response using blockette 62 stage 0
if not response.response_stages and response.instrument_polynomial:
coefficients = response.instrument_polynomial.coefficients
self.data = np.poly1d(coefficients[::-1])(self.data)
return self
# polynomial response using blockette 62 stage 1 and no other stages
if len(response.response_stages) == 1 and isinstance(response.response_stages[0], PolynomialResponseStage):
# check for gain
if response.response_stages[0].stage_gain is None:
msg = 'Stage gain not defined for %s - setting it to 1.0'
warnings.warn(msg % self.id)
gain = 1
else:
gain = response.response_stages[0].stage_gain
coefficients = response.response_stages[0].coefficients[:]
for i in range(len(coefficients)):
coefficients[i] /= math.pow(gain, i)
self.data = np.poly1d(coefficients[::-1])(self.data)
return self
# use evalresp
data = self.data.astype(np.float64)
npts = len(data)
# time domain pre-processing
if zero_mean:
data -= data.mean()
if taper:
data *= cosine_taper(npts, taper_fraction,
sactaper=True, halfcosine=False)
if plot:
fontsz = 12
color1 = "blue"
color2 = "red"
bbox = dict(boxstyle="round", fc="w", alpha=1, ec="w")
bbox1 = dict(boxstyle="round", fc="blue", alpha=0.15)
bbox2 = dict(boxstyle="round", fc="red", alpha=0.15)
if fig is None:
fig = plt.figure(figsize=(14, 10))
fig.suptitle(str(self), fontsize=fontsz)
ax1 = fig.add_subplot(321)
ax1b = ax1.twinx()
ax2 = fig.add_subplot(323, sharex=ax1)
ax2b = ax2.twinx()
ax3 = fig.add_subplot(325, sharex=ax1)
ax3b = ax3.twinx()
ax4 = fig.add_subplot(322)
ax5 = fig.add_subplot(324, sharex=ax4)
ax6 = fig.add_subplot(326, sharex=ax4)
for ax_ in (ax1, ax2, ax3, ax4, ax5, ax6):
ax_.grid(zorder=-10)
if pre_filt is None:
text = 'pre_filt: None'
else:
text = 'pre_filt: [{:.3g}, {:.3g}, {:.3g}, {:.3g}]'.format(
*pre_filt)
ax1.text(0.05, 0.1, text, ha="left", va="bottom",
transform=ax1.transAxes, fontsize=fontsz, bbox=bbox,
zorder=5)
ax1.set_ylabel("Data spectrum, raw", bbox=bbox1, fontsize=fontsz)
ax1b.set_ylabel("'pre_filt' taper fraction", bbox=bbox2, fontsize=fontsz)
evalresp_info = "\n".join(
['output: %s' % output] +
['%s: %s' % (key, value) for key, value in kwargs.items()])
ax2.text(0.05, 0.1, evalresp_info, ha="left",
va="bottom", transform=ax2.transAxes, zorder=5, bbox=bbox, fontsize=fontsz)
ax2.set_ylabel("Data spectrum,\n"
"'pre_filt' applied", bbox=bbox1, fontsize=fontsz)
ax2b.set_ylabel("Instrument response", bbox=bbox2, fontsize=fontsz)
ax3.text(0.05, 0.1, 'water_level: %s' % water_level,
ha="left", va="bottom", transform=ax3.transAxes,
fontsize=fontsz, zorder=5, bbox=bbox)
ax3.set_ylabel("Data spectrum,\nmultiplied with inverted\n"
"instrument response", bbox=bbox1, fontsize=fontsz)
ax3b.set_ylabel("Inverted instrument response,\n"
"water level applied", bbox=bbox2, fontsize=fontsz)
ax3.set_xlabel("Frequency [Hz]", fontsize=fontsz)
times = self.times()
ax4.plot(times, self.data, color="k")
ax4.set_ylabel("Raw", fontsize=fontsz)
ax4.yaxis.set_ticks_position("right")
ax4.yaxis.set_label_position("right")
ax5.plot(times, data, color="k")
ax5.set_ylabel("Raw, after time\ndomain pre-processing", fontsize=fontsz)
ax5.yaxis.set_ticks_position("right")
ax5.yaxis.set_label_position("right")
ax6.set_ylabel("Response removed", fontsize=fontsz)
ax6.set_xlabel("Time [s]", fontsize=fontsz)
ax6.yaxis.set_ticks_position("right")
ax6.yaxis.set_label_position("right")
ax1.tick_params(labelsize=fontsz)
ax1b.tick_params(labelsize=fontsz)
ax2.tick_params(labelsize=fontsz)
ax2b.tick_params(labelsize=fontsz)
ax3.tick_params(labelsize=fontsz)
ax3b.tick_params(labelsize=fontsz)
ax4.tick_params(labelsize=fontsz)
ax5.tick_params(labelsize=fontsz)
ax6.tick_params(labelsize=fontsz)
# smart calculation of nfft dodging large primes
from obspy.signal.util import _npts2nfft
nfft = _npts2nfft(npts)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
# calculate and apply frequency response,
# optionally prefilter in frequency domain and/or apply water level
freq_response, freqs = response.get_evalresp_response(self.stats.delta, nfft,
output=output, **kwargs)
if plot:
ax1.loglog(freqs, np.abs(data), color=color1, zorder=9, label= "Data")
ax1.legend(loc = "upper left")
# frequency domain pre-filtering of data spectrum
# (apply cosine taper in frequency domain)
if pre_filt:
freq_domain_taper = cosine_sac_taper(freqs, flimit=pre_filt)
data *= freq_domain_taper
if plot:
try:
freq_domain_taper
except NameError:
freq_domain_taper = np.ones(len(freqs))
ax1b.semilogx(freqs, freq_domain_taper, color=color2, zorder=10)
ax1b.set_ylim(-0.05, 1.05)
ax2.loglog(freqs, np.abs(data), color=color1, zorder=9, label = "Data")
ax2b.loglog(freqs, np.abs(freq_response), color=color2, zorder=10, label = "Filter")
ax2b.legend(loc = "upper left")
if water_level is None:
# No water level used, so just directly invert the response.
# First entry is at zero frequency and value is zero, too.
# Just do not invert the first value (and set to 0 to make sure).
freq_response[0] = 0.0
freq_response[1:] = 1.0 / freq_response[1:]
else:
# Invert spectrum with specified water level.
invert_spectrum(freq_response, water_level)
data *= freq_response
data[-1] = abs(data[-1]) + 0.0j
if plot:
ax3.loglog(freqs, np.abs(data), color=color1, zorder=9, label = "Data")
ax3b.loglog(freqs, np.abs(freq_response), color=color2, zorder=10, label = "Filter")
# transform data back into the time domain
data = np.fft.irfft(data)[0:npts]
if plot:
# Oftentimes raises NumPy warnings which we don't want to see.
with np.errstate(all="ignore"):
ax6.plot(times, data, color="k")
plt.subplots_adjust(wspace=0.4)
if plot is True and fig is None:
plt.show()
elif plot is True and fig is not None:
pass
else:
plt.savefig(plot)
plt.close(fig)
# assign processed data and store processing information
self.data = data
return self, np.abs(freq_response)
def process_synt(datadir, station, event = None, stationxml_dir = None, period_band = None, npts=None,
sampling_rate=None, output_dir=None, suffix=None):
# ensemble the stream
#station_list = generate_station_list(datadir)
#for station in station_list:
zdatafile = station[0] + "." + station[1] + ".MXZ.sem.sac"
ndatafile = station[0] + "." + station[1] + ".MXN.sem.sac"
edatafile = station[0] + "." + station[1] + ".MXE.sem.sac"
zpath = os.path.join(datadir, zdatafile)
npath = os.path.join(datadir, ndatafile)
epath = os.path.join(datadir, edatafile)
st = read(zpath)
st2 = read(npath)
st3 = read(epath)
#print st
#print st2
st.append(st2[0])
st.append(st3[0])
#print "\nProcessing file: %s" %filename
# interpolation value
#npts = 3630
#sampling_rate = 1.0 # Hz
min_period = period_band[0]
max_period = period_band[1]
f2 = 1.0 / max_period
f3 = 1.0 / min_period
f1 = 0.8 * f2
f4 = 1.2 * f3
pre_filt = (f1, f2, f3, f4)
# fetch event information
event_name = get_event_name(event)
short_event_name = adjust_event_name(event_name)
origin = event.preferred_origin() or event.origins[0]
event_latitude = origin.latitude
event_longitude = origin.longitude
event_time = origin.time
event_depth = origin.depth
starttime = event_time
print "event_time:",event_time
#output_path = os.path.join(output_dir, short_event_name)
if not os.path.exists(output_dir):
os.makedirs(output_dir)
nrecords = len(st)
# processing
for i, tr in enumerate(st):
#get component name
cmpname = tr.stats.channel
#print tr.stats
#tr.interpolate(sampling_rate=sampling_rate, starttime=starttime,
# npts=npts)
#tr.decimate(4, strict_length=False,no_filter=True)
print "Processing %d of total %d" %(i+1, nrecords)
print "Detrend, Demean and Taper..."
tr.detrend("linear")
tr.detrend("demean")
tr.taper(max_percentage=0.05, type="hann")
#print "response show:"
#print tr.stats.response
# Perform a frequency domain taper like during the response removal
# just without an actual response...
#for tr in st:
print "Filtering..."
data = tr.data.astype(np.float64)
# smart calculation of nfft dodging large primes
from obspy.signal.util import _npts2nfft
nfft = _npts2nfft(len(data))
fy = 1.0 / (tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
data *= c_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:len(data)]
# assign processed data and store processing information
tr.data = data
print "Detrend, Demean and Taper again..."
tr.detrend("linear")
tr.detrend("demean")
tr.taper(max_percentage=0.05, type="hann")
print "Interpolate..."
try:
tr.interpolate(sampling_rate=sampling_rate, starttime=starttime,
npts=npts)
except:
print "Error"
return
# rotate
station_latitude = st[0].stats.sac['stla']
station_longitude = st[0].stats.sac['stlo']
event_latitude = st[0].stats.sac['evla']
event_longitude = st[0].stats.sac['evlo']
#print station_latitude, station_longitude
#print station_latitude, station_longitude
_, baz, _ = gps2DistAzimuth(station_latitude, station_longitude,
event_latitude, event_longitude)
print st
st.rotate(method="NE->RT", back_azimuth=baz)
# write out
print st
for tr in st:
comp = tr.stats.channel
outfn = station[0] + "." + station[1] + "." + comp + ".sac"
if suffix is not None and suffix != "":
outfn = outfn + "." + suffix
outpath = os.path.join(output_dir, outfn)
print "file saved:", outpath
tr.stats.sac['b'] = 0
tr.stats.sac['iztype'] = 9
tr.write(outpath, format="SAC")
#-----directory to station list and response files--------
#resp_dir = '/Users/chengxin/Documents/Harvard/Kanto_basin/instrument/resp_all'
#locations = '/Users/chengxin/Documents/Harvard/Kanto_basin/code/KANTO/locations.txt'
resp_dir = '/Users/chengxin/Documents/Harvard/Kanto_basin/code/KANTO/instrument/resp_4types'
locations = '/Users/chengxin/Documents/Harvard/Kanto_basin/code/KANTO/instrument/resp_4types/station.lst'
#-----common variables for extracting resp using evalresp function------
water_level = 60
prefilt = [0.04, 0.05, 2, 3]
downsamp_freq = 20
dt = 1 / downsamp_freq
cc_len = 3600
step = 1800
npts = cc_len * downsamp_freq * 24
Nfft = _npts2nfft(npts)
tdate = obspy.UTCDateTime("2011-11-3T16:30:00.000")
#-----read the station list------
locs = pd.read_csv(locations)
nsta = len(locs)
for ii in range(nsta):
station = locs.iloc[ii]['station']
network = locs.iloc[ii]['network']
print('work on station ' + station)
tfiles = glob.glob(os.path.join(resp_dir, 'RESP.' + station + '*'))
if len(tfiles) == 0:
print('cannot find resp files for station ' + station)
def _remove_response_trace(trace,
inventory=None,
output="VEL",
pre_filt=None,
zero_mean=True,
taper=True,
taper_fraction=0.05,
**kwargs):
response = trace._get_response(inventory)
# polynomial response using blockette 62 stage 0
if not response.response_stages and response.instrument_polynomial:
coefficients = response.instrument_polynomial.coefficients
trace.data = np.poly1d(coefficients[::-1])(trace.data)
return trace
# polynomial response using blockette 62 stage 1 and no other stages
if len(response.response_stages) == 1 and isinstance(
response.response_stages[0], PolynomialResponseStage):
# check for gain
if response.response_stages[0].stage_gain is None:
msg = 'Stage gain not defined for %s - setting it to 1.0'
warnings.warn(msg % trace.id)
gain = 1
else:
gain = response.response_stages[0].stage_gain
coefficients = response.response_stages[0].coefficients[:]
for i in range(len(coefficients)):
coefficients[i] /= np.pow(gain, i)
trace.data = np.poly1d(coefficients[::-1])(trace.data)
return trace
# use evalresp
data = trace.data.astype(np.float64)
npts = len(data)
# time domain pre-processing
if zero_mean:
data -= data.mean()
if taper:
data *= cosine_taper(npts,
taper_fraction,
sactaper=True,
halfcosine=False)
nfft = _npts2nfft(npts)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
# calculate and apply frequency response,
# optionally prefilter in frequency domain and/or apply water level
freq_response, freqs = response.get_evalresp_response(trace.stats.delta,
nfft,
output=output,
**kwargs)
if pre_filt:
freq_domain_taper = cosine_sac_taper(freqs, flimit=pre_filt)
data *= freq_domain_taper
freq_response[0] = 0.0
freq_response[1:] = 1.0 / freq_response[1:]
data *= freq_response
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:npts]
# assign processed data and store processing information
trace.data = data
return trace
trE.data=simulate_seismometer(trE.data, 100, paz_remove=None, paz_simulate=None, remove_sensitivity=True, simulate_sensitivity=True, water_level=wt, taper=True, taper_fraction=tpf, pre_filt=pre_filt, seedresp=seedrespN, nfft_pow2=False)
#trE.simulate(paz_remove=None, pre_filt=pre_filt, seedresp=seedrespE)
# trN.plot(outfile='espectros/Swave_%s_%s.png' % (units,trN.stats.station))
#trN.plot()
#==================================================================================================================
#========= #Calculando la transformada de fourier ==============================================================
#==================================================================================================================
#spectrum=mper(trN.data,200,np.size(trN.data))
n=np.size(trN.data)
#dt=0.01
t=np.linspace(0,n-1,n)*dt
df=1/(n*dt)
freq=np.linspace(0,(n+1)/2,(n+1)/2)*df
nfft = _npts2nfft(n)
specN=np.fft.rfft(trN.data,n=nfft)
specE=np.fft.rfft(trE.data,n=nfft)
Hspec=np.sqrt((specN**2+specE**2)/2)
smooth_Hspec=smooth(Hspec,smth)
#Graficando log-espectro
# plt.plot(np.log10(freq),np.log10(abs(smooth_Hspec)),'k')
# plt.title('Espectro de desplazamiento onda S '+trN.stats.station)
# plt.xlim(0,2)
# plt.ylabel('log(A)')
# plt.xlabel('log(frecuencia [Hz])')
# plt.savefig("espectros/espectroH_SMOOTH10_%s.png" % (trN.stats.station))
#plt.show()
'''
hfile = '/Users/chengxin/Documents/Harvard/Kanto_basin/code/KANTO/CCF_C3/2010_01_11.h5'
with pyasdf.ASDFDataSet(hfile, mode='r') as ds:
data_types = ds.auxiliary_data.list()
#-----take the first data_type-----
data_type = data_types[2]
paths = ds.auxiliary_data[data_type].list()
path = paths[2]
data = ds.auxiliary_data[data_type][path].data[:]
npts = len(data)
#----do fft----
nfft2 = _npts2nfft(npts)
nfft1 = int(next_fast_len(npts))
nfft3 = int(next_fast_len(npts * 2 + 1))
print('nfft1 and nfft2 %d %d' % (nfft1, nfft2))
t0 = time.time()
spec1 = scipy.fftpack.fft(data, nfft1)
wave1 = scipy.fftpack.ifft(spec1, nfft1)
t1 = time.time()
spec2 = np.fft.rfft(data, nfft2)
wave2 = np.fft.irfft(spec2, nfft2)
t2 = time.time()
spec3 = scipy.fftpack.fft(data, nfft3)
wave3 = scipy.fftpack.ifft(spec3, nfft3)
t3 = time.time()
print('fft and rfft takes %f s, %f s and %f s' %
def simulate_seismometer(
data, samp_rate, paz_remove=None, paz_simulate=None,
remove_sensitivity=True, simulate_sensitivity=True, water_level=600.0,
zero_mean=True, taper=True, taper_fraction=0.05, pre_filt=None,
seedresp=None, nfft_pow2=False, pitsasim=True, sacsim=False,
shsim=False):
"""
Simulate/Correct seismometer.
:type data: NumPy :class:`~numpy.ndarray`
:param data: Seismogram, detrend before hand (e.g. zero mean)
:type samp_rate: float
:param samp_rate: Sample Rate of Seismogram
:type paz_remove: dict, None
:param paz_remove: Dictionary containing keys 'poles', 'zeros', 'gain'
(A0 normalization factor). poles and zeros must be a list of complex
floating point numbers, gain must be of type float. Poles and Zeros are
assumed to correct to m/s, SEED convention. Use None for no inverse
filtering.
:type paz_simulate: dict, None
:param paz_simulate: Dictionary containing keys 'poles', 'zeros', 'gain'.
Poles and zeros must be a list of complex floating point numbers, gain
must be of type float. Or None for no simulation.
:type remove_sensitivity: bool
:param remove_sensitivity: Determines if data is divided by
`paz_remove['sensitivity']` to correct for overall sensitivity of
recording instrument (seismometer/digitizer) during instrument
correction.
:type simulate_sensitivity: bool
:param simulate_sensitivity: Determines if data is multiplied with
`paz_simulate['sensitivity']` to simulate overall sensitivity of
new instrument (seismometer/digitizer) during instrument simulation.
:type water_level: float
:param water_level: Water_Level for spectrum to simulate
:type zero_mean: bool
:param zero_mean: If true the mean of the data is subtracted
:type taper: bool
:param taper: If true a cosine taper is applied.
:type taper_fraction: float
:param taper_fraction: Taper fraction of cosine taper to use
:type pre_filt: list or tuple of floats
:param pre_filt: Apply a bandpass filter to the data trace before
deconvolution. The list or tuple defines the four corner frequencies
(f1,f2,f3,f4) of a cosine taper which is one between f2 and f3 and
tapers to zero for f1 < f < f2 and f3 < f < f4.
:type seedresp: dict, None
:param seedresp: Dictionary contains keys 'filename', 'date', 'units'.
'filename' is the path to a RESP-file generated from a dataless SEED
volume (or a file like object with RESP information);
'date' is a :class:`~obspy.core.utcdatetime.UTCDateTime` object for the
date that the response function should be extracted for (can be omitted
when calling simulate() on Trace/Stream. the Trace's starttime will
then be used);
'units' defines the units of the response function.
Can be either 'DIS', 'VEL' or 'ACC'.
:type nfft_pow2: bool
:param nfft_pow2: Number of frequency points to use for FFT. If True,
the exact power of two is taken (default in PITSA). If False the
data are not zero-padded to the next power of two which makes a
slower FFT but is then much faster for e.g. evalresp which scales
with the FFT points.
:type pitsasim: bool
:param pitsasim: Choose parameters to match
instrument correction as done by PITSA.
:type sacsim: bool
:param sacsim: Choose parameters to match
instrument correction as done by SAC.
:type shsim: bool
:param shsim: Choose parameters to match
instrument correction as done by Seismic Handler.
:return: The corrected data are returned as :class:`numpy.ndarray` float64
array. float64 is chosen to avoid numerical instabilities.
This function works in the frequency domain, where nfft is the next power
of len(data) to avoid wrap around effects during convolution. The inverse
of the frequency response of the seismometer (``paz_remove``) is
convolved with the spectrum of the data and with the frequency response
of the seismometer to simulate (``paz_simulate``). A 5% cosine taper is
taken before simulation. The data must be detrended (e.g.) zero mean
beforehand. If paz_simulate=None only the instrument correction is done.
In the latter case, a broadband filter can be applied to the data trace
using pre_filt. This restricts the signal to the valid frequency band and
thereby avoids artifacts due to amplification of frequencies outside of the
instrument's passband (for a detailed discussion see
*Of Poles and Zeros*, F. Scherbaum, Kluwer Academic Publishers).
.. versionchanged:: 0.5.1
The default for `remove_sensitivity` and `simulate_sensitivity` has
been changed to ``True``. Old deprecated keyword arguments `paz`,
`inst_sim`, `no_inverse_filtering` have been removed.
"""
# Checking the types
if not paz_remove and not paz_simulate and not seedresp:
msg = "Neither inverse nor forward instrument simulation specified."
raise TypeError(msg)
for d in [paz_remove, paz_simulate]:
if d is None:
continue
for key in ['poles', 'zeros', 'gain']:
if key not in d:
raise KeyError("Missing key: %s" % key)
# Translated from PITSA: spr_resg.c
delta = 1.0 / samp_rate
#
ndat = len(data)
data = data.astype(np.float64)
if zero_mean:
data -= data.mean()
if taper:
if sacsim:
data *= cosine_taper(ndat, taper_fraction,
sactaper=sacsim, halfcosine=False)
else:
data *= cosine_taper(ndat, taper_fraction)
# The number of points for the FFT has to be at least 2 * ndat (in
# order to prohibit wrap around effects during convolution) cf.
# Numerical Recipes p. 429 calculate next power of 2.
if nfft_pow2:
nfft = util.next_pow_2(2 * ndat)
# evalresp scales directly with nfft, therefore taking the next power of
# two has a greater negative performance impact than the slow down of a
# not power of two in the FFT
else:
nfft = _npts2nfft(ndat)
# Transform data in Fourier domain
data = np.fft.rfft(data, n=nfft)
# Inverse filtering = Instrument correction
if paz_remove:
freq_response, freqs = paz_to_freq_resp(
paz_remove['poles'], paz_remove['zeros'], paz_remove['gain'],
delta, nfft, freq=True)
if seedresp:
freq_response, freqs = evalresp(delta, nfft, seedresp['filename'],
seedresp['date'],
units=seedresp['units'], freq=True,
network=seedresp['network'],
station=seedresp['station'],
locid=seedresp['location'],
channel=seedresp['channel'])
if not remove_sensitivity:
msg = "remove_sensitivity is set to False, but since seedresp " + \
"is selected the overall sensitivity will be corrected " + \
" for anyway!"
warnings.warn(msg)
if paz_remove or seedresp:
if pre_filt:
# make cosine taper
fl1, fl2, fl3, fl4 = pre_filt
if sacsim:
cos_win = cosine_sac_taper(freqs, flimit=(fl1, fl2, fl3, fl4))
else:
cos_win = cosine_taper(freqs.size, freqs=freqs,
flimit=(fl1, fl2, fl3, fl4))
data *= cos_win
invert_spectrum(freq_response, water_level)
data *= freq_response
del freq_response
# Forward filtering = Instrument simulation
if paz_simulate:
data *= paz_to_freq_resp(paz_simulate['poles'], paz_simulate['zeros'],
paz_simulate['gain'], delta, nfft)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:ndat]
if pitsasim:
# linear detrend
data = simple_detrend(data)
if shsim:
# detrend using least squares
data = scipy.signal.detrend(data, type="linear")
# correct for involved overall sensitivities
if paz_remove and remove_sensitivity and not seedresp:
data /= paz_remove['sensitivity']
if paz_simulate and simulate_sensitivity:
data *= paz_simulate['sensitivity']
return data
def remove_response(trace,
inventory=None,
output="VEL",
water_level=60,
pre_filt=None,
zero_mean=True,
taper=True,
taper_fraction=0.05,
plot=False,
fig=None,
return_spectra=False,
**kwargs):
"""
Deconvolve instrument response. Based on a method on trace.
It adds units, which are obviously dependent on the problem.
axis ax5b is modified to show the pre-filtered trace instead of the
time domain pre filter.
Uses the adequate :class:`obspy.core.inventory.response.Response`
from the provided
:class:`obspy.core.inventory.inventory.Inventory` data. Raises an
exception if the response is not present.
Note that there are two ways to prevent overamplification
while convolving the inverted instrument spectrum: One possibility is
to specify a water level which represents a clipping of the inverse
spectrum and limits amplification to a certain maximum cut-off value
(`water_level` in dB). The other possibility is to taper the waveform
data in the frequency domain prior to multiplying with the inverse
spectrum, i.e. perform a pre-filtering in the frequency domain
(specifying the four corner frequencies of the frequency taper as a
tuple in `pre_filt`).
.. note::
Any additional kwargs will be passed on to
:meth:`obspy.core.inventory.response.Response.get_evalresp_response`,
see documentation of that method for further customization (e.g.
start/stop stage).
.. note::
Using :meth:`~Trace.remove_response` is equivalent to using
:meth:`~Trace.simulate` with the identical response provided as
a (dataless) SEED or RESP file and when using the same
`water_level` and `pre_filt` (and options `sacsim=True` and
`pitsasim=False` which influence very minor details in detrending
and tapering).
.. rubric:: Example
>>> from obspy import read, read_inventory
>>> st = read()
>>> tr = st[0].copy()
>>> inv = read_inventory()
>>> tr.remove_response(inventory=inv) # doctest: +ELLIPSIS
<...Trace object at 0x...>
>>> tr.plot() # doctest: +SKIP
.. plot::
from obspy import read, read_inventory
st = read()
tr = st[0]
inv = read_inventory()
tr.remove_response(inventory=inv)
tr.plot()
Using the `plot` option it is possible to visualize the individual
steps during response removal in the frequency domain to check the
chosen `pre_filt` and `water_level` options to stabilize the
deconvolution of the inverted instrument response spectrum:
>>> from obspy import read, read_inventory
>>> st = read("/path/to/IU_ULN_00_LH1_2015-07-18T02.mseed")
>>> tr = st[0]
>>> inv = read_inventory("/path/to/IU_ULN_00_LH1.xml")
>>> pre_filt = [0.001, 0.005, 45, 50]
>>> tr.remove_response(inventory=inv, pre_filt=pre_filt, output="DISP",
... water_level=60, plot=True) # doctest: +SKIP
<...Trace object at 0x...>
.. plot::
from obspy import read, read_inventory
st = read("/path/to/IU_ULN_00_LH1_2015-07-18T02.mseed", "MSEED")
tr = st[0]
inv = read_inventory("/path/to/IU_ULN_00_LH1.xml", "STATIONXML")
pre_filt = [0.001, 0.005, 45, 50]
output = "DISP"
tr.remove_response(inventory=inv, pre_filt=pre_filt, output=output,
water_level=60, plot=True)
:type inventory: :class:`~obspy.core.inventory.inventory.Inventory`
or None.
:param inventory: Station metadata to use in search for adequate
response. If inventory parameter is not supplied, the response
has to be attached to the trace with :meth:`Trace.attach_response`
beforehand.
:type output: str
:param output: Output units. One of:
``"DISP"``
displacement, output unit is meters
``"VEL"``
velocity, output unit is meters/second
``"ACC"``
acceleration, output unit is meters/second**2
:type water_level: float
:param water_level: Water level for deconvolution.
:type pre_filt: list or tuple of four float
:param pre_filt: Apply a bandpass filter in frequency domain to the
data before deconvolution. The list or tuple defines
the four corner frequencies `(f1, f2, f3, f4)` of a cosine taper
which is one between `f2` and `f3` and tapers to zero for
`f1 < f < f2` and `f3 < f < f4`.
:type zero_mean: bool
:param zero_mean: If `True`, the mean of the waveform data is
subtracted in time domain prior to deconvolution.
:type taper: bool
:param taper: If `True`, a cosine taper is applied to the waveform data
in time domain prior to deconvolution.
:type taper_fraction: float
:param taper_fraction: Taper fraction of cosine taper to use.
:type plot: bool or str
:param plot: If `True`, brings up a plot that illustrates how the
data are processed in the frequency domain in three steps. First by
`pre_filt` frequency domain tapering, then by inverting the
instrument response spectrum with or without `water_level` and
finally showing data with inverted instrument response multiplied
on it in frequency domain. It also shows the comparison of
raw/corrected data in time domain. If a `str` is provided then the
plot is saved to file (filename must have a valid image suffix
recognizable by matplotlib e.g. '.png').
"""
limit_numpy_fft_cache()
from obspy.core.inventory import PolynomialResponseStage
from obspy.signal.invsim import (cosine_taper, cosine_sac_taper,
invert_spectrum)
if plot:
import matplotlib.pyplot as plt
if (isinstance(inventory, (str, native_str))
and inventory.upper() in ("DISP", "VEL", "ACC")):
from obspy.core.util.deprecation_helpers import \
ObsPyDeprecationWarning
output = inventory
inventory = None
msg = ("The order of optional parameters in method "
"remove_response has changed. 'output' is not accepted "
"as first positional argument in the next release.")
warnings.warn(msg, category=ObsPyDeprecationWarning, stacklevel=3)
response = trace._get_response(inventory)
# polynomial response using blockette 62 stage 0
if not response.response_stages and response.instrument_polynomial:
coefficients = response.instrument_polynomial.coefficients
trace.data = np.poly1d(coefficients[::-1])(trace.data)
return trace
# polynomial response using blockette 62 stage 1 and no other stages
if len(response.response_stages) == 1 and \
isinstance(response.response_stages[0], PolynomialResponseStage):
# check for gain
if response.response_stages[0].stage_gain is None:
msg = 'Stage gain not defined for %s - setting it to 1.0'
warnings.warn(msg % trace.id)
gain = 1
else:
gain = response.response_stages[0].stage_gain
coefficients = response.response_stages[0].coefficients[:]
for i in range(len(coefficients)):
coefficients[i] /= math.pow(gain, i)
trace.data = np.poly1d(coefficients[::-1])(trace.data)
return trace
# use evalresp
data = trace.data.astype(np.float64)
npts = len(data)
# time domain pre-processing
if zero_mean:
data -= data.mean()
if taper:
data *= cosine_taper(npts,
taper_fraction,
sactaper=True,
halfcosine=False)
if plot:
color1 = "blue"
color2 = "red"
bbox = dict(boxstyle="round", fc="w", alpha=1, ec="w")
bbox1 = dict(boxstyle="round", fc="blue", alpha=0.15)
bbox2 = dict(boxstyle="round", fc="red", alpha=0.15)
if fig is None:
fig = plt.figure(figsize=(14, 10))
fig.suptitle("{}:\nRemoving the Instrument Response".format(
str(trace)),
fontsize=16)
ax1 = fig.add_subplot(321)
ax1b = ax1.twinx()
ax2 = fig.add_subplot(323, sharex=ax1)
ax2b = ax2.twinx()
ax3 = fig.add_subplot(325, sharex=ax1)
ax3b = ax3.twinx()
ax4 = fig.add_subplot(322)
ax5 = fig.add_subplot(324, sharex=ax4)
ax6 = fig.add_subplot(326, sharex=ax4)
for ax_ in (ax1, ax2, ax3, ax4, ax5, ax6):
ax_.grid(zorder=-10)
ax4.set_title("Waveform")
# if pre_filt is not None:
# # text = 'pre_filt: None'
# # else:
output_dict = {
'DISP': 'Displacement',
'VEL': 'Velocity',
'ACC': 'Acceleration'
}
# labels - specific to Apollo data
unit_dict = {
'DISP': 'DU/m',
'VEL': 'DU/(m/s)',
'ACC': r'DU/(m/s$\mathrm{^2}$)'
}
unit_inverse_dict = {
'DISP': 'm/DU',
'VEL': '(m/s)/DU',
'ACC': r'(m/s$\mathrm{^2}$)/DU'
}
unit_final_dict = {
'DISP': 'm',
'VEL': 'm/s',
'ACC': r'm/s$\mathrm{^2}$'
}
raw_unit = 'DU'
ax1.set_ylabel("Raw [{}]".format(raw_unit), bbox=bbox1, fontsize=16)
ax1.yaxis.set_label_coords(-0.13, 0.5)
if pre_filt is not None:
text = 'Pre-filter parameters:\n [{:.3g}, {:.3g}, {:.3g}, {:.3g}]'.format(
*pre_filt)
ax1.text(0.05,
0.1,
text,
ha="left",
va="bottom",
transform=ax1.transAxes,
fontsize="large",
bbox=bbox,
zorder=5)
ax1b.set_ylabel("Pre-filter", bbox=bbox2, fontsize=16)
ax1b.yaxis.set_label_coords(1.14, 0.5)
ax1.set_title("Spectrum", color='b')
output_dict = {
'DISP': 'Displacement',
'VEL': 'Velocity',
'ACC': 'Acceleration'
}
evalresp_info = "\n".join(
['Output: %s' % output_dict[output]] +
['%s: %s' % (key, value) for key, value in kwargs.items()])
ax2.text(0.05,
0.1,
evalresp_info,
ha="left",
va="bottom",
transform=ax2.transAxes,
fontsize="large",
zorder=5,
bbox=bbox)
ax2.set_ylabel("Pre-processed [{}]".format(raw_unit),
bbox=bbox1,
fontsize=16)
ax2.yaxis.set_label_coords(-0.13, 0.5)
ax2b.set_ylabel("Instrument\nresponse [{}]".format(unit_dict[output]),
bbox=bbox2,
fontsize=16)
ax2b.yaxis.set_label_coords(1.14, 0.5)
if water_level is not None:
ax3.text(0.05,
0.1,
"Water Level: %s" % water_level,
ha="left",
va="bottom",
transform=ax3.transAxes,
fontsize="large",
zorder=5,
bbox=bbox)
ax3.set_ylabel("Multiplied with inverted\n"
"instrument response [{}]".format(
unit_final_dict[output]),
bbox=bbox1,
fontsize=16)
ax3.yaxis.set_label_coords(-0.13, 0.5)
if water_level is not None:
ax3b.set_ylabel("Inverted instrument response,\n"
"water level applied [{}]".format(
unit_inverse_dict[output]),
bbox=bbox2,
fontsize=16)
else:
ax3b.set_ylabel("Inverted instrument\nresponse [{}]".format(
unit_inverse_dict[output]),
bbox=bbox2,
fontsize=16)
ax3b.yaxis.set_label_coords(1.14, 0.5)
# xlbl = ax3b.yaxis.get_label()
# print(xlbl.get_position())
#
#
# xlbl = ax3b.yaxis.get_label()
# print(xlbl.get_position())
ax3.set_xlabel("Frequency [Hz]")
times = trace.times()
ax4.plot(times, trace.data, color="k")
ax4.set_ylabel("Raw [{}]".format(raw_unit), fontsize=16)
ax4.yaxis.set_ticks_position("right")
ax4.yaxis.set_label_position("right")
ax4.yaxis.set_label_coords(1.14, 0.5)
# Ceri
# ax5.plot(times, data, color="k")
ax5.set_ylabel("Pre-processed [{}]".format(raw_unit), fontsize=16)
ax5.yaxis.set_ticks_position("right")
ax5.yaxis.set_label_position("right")
ax5.yaxis.set_label_coords(1.14, 0.5)
ax6.set_ylabel("Response removed [{}]".format(unit_final_dict[output]),
fontsize=16)
ax6.set_xlabel("Time [s]")
ax6.yaxis.set_ticks_position("right")
ax6.yaxis.set_label_position("right")
ax6.yaxis.set_label_coords(1.14, 0.5)
# smart calculation of nfft dodging large primes
from obspy.signal.util import _npts2nfft
nfft = _npts2nfft(npts)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
# calculate and apply frequency response,
# optionally prefilter in frequency domain and/or apply water level
freq_response, freqs = \
response.get_evalresp_response(trace.stats.delta, nfft,
output=output, **kwargs)
if plot:
ax1.loglog(freqs, np.abs(data), color=color1, zorder=9)
# frequency domain pre-filtering of data spectrum
# (apply cosine taper in frequency domain)
if pre_filt:
freq_domain_taper = cosine_sac_taper(freqs, flimit=pre_filt)
data *= freq_domain_taper
if plot:
try:
freq_domain_taper
except NameError:
freq_domain_taper = np.ones(len(freqs))
if pre_filt is not None:
ax1b.semilogx(freqs, freq_domain_taper, color=color2, zorder=10)
ax1b.set_ylim(-0.05, 1.05)
ax2.loglog(freqs, np.abs(data), color=color1, zorder=9)
ax2b.loglog(freqs, np.abs(freq_response), color=color2, zorder=10)
# Ceri - transform data back into the time domain - just to view it
filt_data = np.fft.irfft(data)[0:npts]
ax5.plot(times, filt_data, color="k")
if water_level is None:
# No water level used, so just directly invert the response.
# First entry is at zero frequency and value is zero, too.
# Just do not invert the first value (and set to 0 to make sure).
freq_response[0] = 0.0
freq_response[1:] = 1.0 / freq_response[1:]
else:
# Invert spectrum with specified water level.
invert_spectrum(freq_response, water_level)
data *= freq_response
data[-1] = abs(data[-1]) + 0.0j
spectra = np.abs(data)
if plot:
ax3.loglog(freqs, np.abs(data), color=color1, zorder=9)
ax3b.loglog(freqs, np.abs(freq_response), color=color2, zorder=10)
# transform data back into the time domain
data = np.fft.irfft(data)[0:npts]
if plot:
# Oftentimes raises NumPy warnings which we don't want to see.
with np.errstate(all="ignore"):
ax6.plot(times, data, color="k")
plt.subplots_adjust(wspace=0.4)
if plot is True and fig is None:
plt.show()
elif plot is True and fig is not None:
# Ceri - changed this so that the graph does actually show
plt.show()
else:
plt.savefig(plot)
plt.close(fig)
# assign processed data and store processing information
trace.data = data
if return_spectra:
return trace, freqs, spectra
else:
return trace
if source.stats.npts != downsamp_freq * 24 * cc_len:
print(
'Moving to next: extraced response file does not match the sac length'
)
continue
#-----load the instrument response nyc file-----
resp_file = os.path.join(resp_dir,
'resp.' + station + '.npy')
respz = np.load(resp_file)
if not os.path.isfile(resp_file):
print("no instrument response for " + station)
continue
#----------do fft now----------
nfft = _npts2nfft(source.stats.npts)
source_spect = np.fft.rfft(source.data, n=nfft)
fy = 1 / (dt * 2.0)
freq = np.linspace(0, fy, nfft // 2 + 1)
#-----apply a cosine taper to target freq-----
#cos_win = cosine_sac_taper(freq, flimit=pre_filt)
#source_spect *=cos_win
source_spect *= respz
source.data = np.fft.irfft(
source_spect)[0:source.stats.npts]
source.data = bandpass(source.data,
freqmin,
freqmax,
downsamp_freq,
def simulate_seismometer(data,
samp_rate,
paz_remove=None,
paz_simulate=None,
remove_sensitivity=True,
simulate_sensitivity=True,
water_level=600.0,
zero_mean=True,
taper=True,
taper_fraction=0.05,
pre_filt=None,
seedresp=None,
nfft_pow2=False,
pitsasim=True,
sacsim=False,
shsim=False):
"""
Simulate/Correct seismometer.
:type data: NumPy :class:`~numpy.ndarray`
:param data: Seismogram, detrend before hand (e.g. zero mean)
:type samp_rate: float
:param samp_rate: Sample Rate of Seismogram
:type paz_remove: dict, None
:param paz_remove: Dictionary containing keys 'poles', 'zeros', 'gain'
(A0 normalization factor). poles and zeros must be a list of complex
floating point numbers, gain must be of type float. Poles and Zeros are
assumed to correct to m/s, SEED convention. Use None for no inverse
filtering.
:type paz_simulate: dict, None
:param paz_simulate: Dictionary containing keys 'poles', 'zeros', 'gain'.
Poles and zeros must be a list of complex floating point numbers, gain
must be of type float. Or None for no simulation.
:type remove_sensitivity: bool
:param remove_sensitivity: Determines if data is divided by
`paz_remove['sensitivity']` to correct for overall sensitivity of
recording instrument (seismometer/digitizer) during instrument
correction.
:type simulate_sensitivity: bool
:param simulate_sensitivity: Determines if data is multiplied with
`paz_simulate['sensitivity']` to simulate overall sensitivity of
new instrument (seismometer/digitizer) during instrument simulation.
:type water_level: float
:param water_level: Water_Level for spectrum to simulate
:type zero_mean: bool
:param zero_mean: If true the mean of the data is subtracted
:type taper: bool
:param taper: If true a cosine taper is applied.
:type taper_fraction: float
:param taper_fraction: Taper fraction of cosine taper to use
:type pre_filt: list or tuple of floats
:param pre_filt: Apply a bandpass filter to the data trace before
deconvolution. The list or tuple defines the four corner frequencies
(f1,f2,f3,f4) of a cosine taper which is one between f2 and f3 and
tapers to zero for f1 < f < f2 and f3 < f < f4.
:type seedresp: dict, None
:param seedresp: Dictionary contains keys 'filename', 'date', 'units'.
'filename' is the path to a RESP-file generated from a dataless SEED
volume (or a file like object with RESP information);
'date' is a :class:`~obspy.core.utcdatetime.UTCDateTime` object for the
date that the response function should be extracted for (can be omitted
when calling simulate() on Trace/Stream. the Trace's starttime will
then be used);
'units' defines the units of the response function.
Can be either 'DIS', 'VEL' or 'ACC'.
:type nfft_pow2: bool
:param nfft_pow2: Number of frequency points to use for FFT. If True,
the exact power of two is taken (default in PITSA). If False the
data are not zero-padded to the next power of two which makes a
slower FFT but is then much faster for e.g. evalresp which scales
with the FFT points.
:type pitsasim: bool
:param pitsasim: Choose parameters to match
instrument correction as done by PITSA.
:type sacsim: bool
:param sacsim: Choose parameters to match
instrument correction as done by SAC.
:type shsim: bool
:param shsim: Choose parameters to match
instrument correction as done by Seismic Handler.
:return: The corrected data are returned as :class:`numpy.ndarray` float64
array. float64 is chosen to avoid numerical instabilities.
This function works in the frequency domain, where nfft is the next power
of len(data) to avoid wrap around effects during convolution. The inverse
of the frequency response of the seismometer (``paz_remove``) is
convolved with the spectrum of the data and with the frequency response
of the seismometer to simulate (``paz_simulate``). A 5% cosine taper is
taken before simulation. The data must be detrended (e.g.) zero mean
beforehand. If paz_simulate=None only the instrument correction is done.
In the latter case, a broadband filter can be applied to the data trace
using pre_filt. This restricts the signal to the valid frequency band and
thereby avoids artifacts due to amplification of frequencies outside of the
instrument's passband (for a detailed discussion see
*Of Poles and Zeros*, F. Scherbaum, Kluwer Academic Publishers).
.. versionchanged:: 0.5.1
The default for `remove_sensitivity` and `simulate_sensitivity` has
been changed to ``True``. Old deprecated keyword arguments `paz`,
`inst_sim`, `no_inverse_filtering` have been removed.
"""
# Checking the types
if not paz_remove and not paz_simulate and not seedresp:
msg = "Neither inverse nor forward instrument simulation specified."
raise TypeError(msg)
for d in [paz_remove, paz_simulate]:
if d is None:
continue
for key in ['poles', 'zeros', 'gain']:
if key not in d:
raise KeyError("Missing key: %s" % key)
# Translated from PITSA: spr_resg.c
delta = 1.0 / samp_rate
#
ndat = len(data)
data = data.astype(np.float64)
if zero_mean:
data -= data.mean()
if taper:
if sacsim:
data *= cosine_taper(ndat,
taper_fraction,
sactaper=sacsim,
halfcosine=False)
else:
data *= cosine_taper(ndat, taper_fraction)
# The number of points for the FFT has to be at least 2 * ndat (in
# order to prohibit wrap around effects during convolution) cf.
# Numerical Recipes p. 429 calculate next power of 2.
if nfft_pow2:
nfft = util.next_pow_2(2 * ndat)
# evalresp scales directly with nfft, therefore taking the next power of
# two has a greater negative performance impact than the slow down of a
# not power of two in the FFT
else:
nfft = _npts2nfft(ndat)
# Transform data in Fourier domain
data = np.fft.rfft(data, n=nfft)
# Inverse filtering = Instrument correction
if paz_remove:
freq_response, freqs = paz_to_freq_resp(paz_remove['poles'],
paz_remove['zeros'],
paz_remove['gain'],
delta,
nfft,
freq=True)
if seedresp:
freq_response, freqs = evalresp(delta,
nfft,
seedresp['filename'],
seedresp['date'],
units=seedresp['units'],
freq=True,
network=seedresp['network'],
station=seedresp['station'],
locid=seedresp['location'],
channel=seedresp['channel'])
if not remove_sensitivity:
msg = "remove_sensitivity is set to False, but since seedresp " + \
"is selected the overall sensitivity will be corrected " + \
" for anyway!"
warnings.warn(msg)
if paz_remove or seedresp:
if pre_filt:
# make cosine taper
fl1, fl2, fl3, fl4 = pre_filt
if sacsim:
cos_win = cosine_sac_taper(freqs, flimit=(fl1, fl2, fl3, fl4))
else:
cos_win = cosine_taper(freqs.size,
freqs=freqs,
flimit=(fl1, fl2, fl3, fl4))
data *= cos_win
invert_spectrum(freq_response, water_level)
data *= freq_response
del freq_response
# Forward filtering = Instrument simulation
if paz_simulate:
data *= paz_to_freq_resp(paz_simulate['poles'], paz_simulate['zeros'],
paz_simulate['gain'], delta, nfft)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:ndat]
if pitsasim:
# linear detrend
data = simple_detrend(data)
if shsim:
# detrend using least squares
data = scipy.signal.detrend(data, type="linear")
# correct for involved overall sensitivities
if paz_remove and remove_sensitivity and not seedresp:
data /= paz_remove['sensitivity']
if paz_simulate and simulate_sensitivity:
data *= paz_simulate['sensitivity']
return data
def process_synthetics(st, freqmax, freqmin):
f2 = 0.9 * freqmin
f3 = 1.1 * freqmax
f1 = 0.5 * f2
f4 = 2.0 * f3
pre_filt = (f1, f2, f3, f4)
# Detrend and taper.
st.detrend("linear")
st.detrend("demean")
st.taper(max_percentage=0.05, type="hann")
# Perform a frequency domain taper like during the response removal
# just without an actual response...
# See function remove_response in trace.py from obspy.
for tr in st:
# Assuming displacement seismograms
tr.differentiate()
data = tr.data.astype(np.float64)
orig_len = len(data)
# smart calculation of nfft dodging large primes
# noinspection PyProtectedMember
from obspy.signal.util import _npts2nfft
nfft = _npts2nfft(len(data))
fy = 1.0 / (tr.stats.delta * 2.0)
freqs = np.linspace(0, fy, nfft // 2 + 1)
# Transform data to Frequency domain
data = np.fft.rfft(data, n=nfft)
# noinspection PyTypeChecker
data *= cosine_sac_taper(freqs, flimit=pre_filt)
data[-1] = abs(data[-1]) + 0.0j
# transform data back into the time domain
data = np.fft.irfft(data)[0:orig_len]
# assign processed data and store processing information
tr.data = data
tr.detrend("linear")
tr.detrend("demean")
tr.taper(0.05, type="cosine")
tr.filter("bandpass",
freqmin=freqmin,
freqmax=freqmax,
corners=3,
zerophase=True)
tr.detrend("linear")
tr.detrend("demean")
tr.taper(0.05, type="cosine")
tr.filter("bandpass",
freqmin=freqmin,
freqmax=freqmax,
corners=3,
zerophase=True)
return st